Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50007

A rainstorm increased the amount of water stored in State J
[#permalink]
Show Tags
30 Jul 2012, 01:47
Question Stats:
71% (02:36) correct 29% (02:45) wrong based on 1456 sessions
HideShow timer Statistics




Math Expert
Joined: 02 Sep 2009
Posts: 50007

Re: A rainstorm increased the amount of water stored in State J
[#permalink]
Show Tags
30 Jul 2012, 01:48
SOLUTIONA rainstorm increased the amount of water stored in State J reservoirs from 124 billion gallons to 138 billion gallons. If the storm increased the amount of water in the reservoirs to 82 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm?(A) 9 (B) 14 (C) 25 (D) 30 (E) 44 Since we need to find only an approximate value and the answer choices are quite widespread, then use: 80% instead of 82% (notice that this approximation gives the bigger tank capacity); 140 billion gallons instead of 138 billion gallons (notice that this approximation also gives the bigger tank capacity); 130 billion gallons instead of 124 billion gallons;. Notice that the third approximation balances the first two a little bit. So, we'll have that: \(capacity*0.8=140\) > \(capacity=\frac{140}{0.8}=175\). Hence, the amount of water the reservoirs were short of total capacity prior to the storm was approximately \(175130=45\) billion gallons. Answer: E.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




Intern
Joined: 27 Jul 2012
Posts: 25

Re: A rainstorm increased the amount of water stored in State J
[#permalink]
Show Tags
30 Jul 2012, 02:25
Currently 138 billion which is 82% of capacity. i.e. Capacity*82%= 138 billion Capacity=\(\frac{138}{82%}\) Capacity=168.3 billion
Thus it was short of 168.3124= 44 billion gallons



Director
Joined: 22 Mar 2011
Posts: 601
WE: Science (Education)

Re: A rainstorm increased the amount of water stored in State J
[#permalink]
Show Tags
30 Jul 2012, 10:03
Bunuel wrote: A rainstorm increased the amount of water stored in State J reservoirs from 124 billion gallons to 138 billion gallons. If the storm increased the amount of water in the reservoirs to 82 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm? (A) 9 (B) 14 (C) 25 (D) 30 (E) 44 Practice Questions Question: 6 Page: 152 Difficulty: 600 Since an approximation is needed, and we cannot use a calculator, I would take that 138 billion represents only 80 percent of the full capacity. I know that my answer will be a slight overshoot. So, if 138 is 80%, then 10% is 138/8 = 34.5/2 = 17.25, and 100% will be 172.5 billion. My overshot answer is 172.5124=48.5. So, the correct answer should be 44. Just to be on the safe side: (124+30)*0.8=154*0.8=123.2 and (124+44)*0.8=168*0.8= 134.4, so definitely, 44 is the correct answer. By a second thought, if we think of "ball parking", then all we need are the last two tests above. It is clear that the answer should be greater than 14 (124+14=138, which is just 82% of full capacity). No need to calculate the full capacity and then the required difference, it is sufficient to check that (124 + the answer) * 0.8 is the closest to 138. Not a pretty question... Answer E
_________________
PhD in Applied Mathematics Love GMAT Quant questions and running.



Manager
Joined: 21 Oct 2013
Posts: 187
Location: Germany
GPA: 3.51

Re: A rainstorm increased the amount of water stored in State J
[#permalink]
Show Tags
17 Jan 2014, 04:31
Calculation approach:
1 % of capacity equals: 138/82 = 1.7 (rounded)gal (since 0.7*82 is slightly greater than 138). 100% of capacity = 100*1.7 = 170 = full capacity of tank.
170124= 46 which is very close to E. Hence E.



Intern
Joined: 24 Aug 2013
Posts: 5

Re: A rainstorm increased the amount of water stored in State J
[#permalink]
Show Tags
25 May 2014, 20:43
A rainstorm increased the amount of water stored in State J reservoirs from 124 billion gallons to 138 billion gallons. If the storm increased the amount of water in the reservoirs to 82 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm?
Solution:
82% * Cap =138 Cap = (138*100)/82 Using approximation: Cap = (136*100)/80
Note: Den and Num decreased, Hence both cancel out each others effect.
Cap =136*(5/4) = 34*5 = 170
Now, 170124 = 46 = ~44 (Nearest answer)



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1829
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: A rainstorm increased the amount of water stored in State J
[#permalink]
Show Tags
25 May 2014, 23:31
82% capacity = 138 Billion Gallons, so 100% = \(138 * \frac{100}{82} = \frac{6900}{41}\) Shortfall before rain = \(\frac{6900}{41}  124\) \(= \frac{1816}{41}\) = 44 (Approx) Answer = E
_________________
Kindly press "+1 Kudos" to appreciate



Intern
Joined: 10 Nov 2012
Posts: 3

Re: A rainstorm increased the amount of water stored in State J
[#permalink]
Show Tags
31 May 2014, 12:14
After the reservoir is filled to 138 gallons the amount of water is at 82% or roughly 80%  which means that 20% of the reservoir is empty. To figure out what that 20% is approximate: 140 gallons /80 percent = x gallons /20 percent , therefore, x = 35 gallons , answer choices A,B,C,D are below 35 . We know that the reservoir must be short more than 35 gallons, therefore, the only possible choice is E.
Thinking about this question visually you see that the # of gallons that the reservoir was originally short = different b/w 138 & 124 + difference b/w total & 138 (138 gallons  124 gallons) + (total gallons  138 gallons)
Eliminate A & B, because the difference b/w 138 & 124 = 14, and after filling up to 138 gallons there is still 18% of space left in the reservoir. Knowing this we know that the answer choice has to be higher than 14 gallons. To figure out how much higher approximate:
138% = 82% we can derive that approximately 140 gallons = 80% ; remaining 20% = 140 * 20/80 = 35 gallons even without doing the calculation any further you can eliminate answer choices C & D because 35 gallons is higher than both C & D.
14 + 35 = 49 gallons



Manager
Joined: 07 Apr 2014
Posts: 115

Re: A rainstorm increased the amount of water stored in State J
[#permalink]
Show Tags
09 Sep 2014, 11:10
Bunuel wrote: A rainstorm increased the amount of water stored in State J reservoirs from 124 billion gallons to 138 billion gallons. If the storm increased the amount of water in the reservoirs to 82 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm? (A) 9 (B) 14 (C) 25 (D) 30 (E) 44 Practice Questions Question: 6 Page: 152 Difficulty: 600 clumsy numbers in the problem.. 138 is 82% of total. then total = (138*100)/82 = appro 168 before the storm it was 124 then 168124 = 44



Intern
Joined: 09 Apr 2014
Posts: 4

Re: A rainstorm increased the amount of water stored in State J
[#permalink]
Show Tags
17 Mar 2015, 06:40
Bunuel wrote: SOLUTION
A rainstorm increased the amount of water stored in State J reservoirs from 124 billion gallons to 138 billion gallons. If the storm increased the amount of water in the reservoirs to 82 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm?
(A) 9 (B) 14 (C) 25 (D) 30 (E) 44
Since we need to find only an approximate value and the answer choices are quite widespread, then use:
80% instead of 82% (notice that this approximation gives the bigger tank capacity); 140 billion gallons instead of 138 billion gallons (notice that this approximation also gives the bigger tank capacity); 130 billion gallons instead of 124 billion gallons;.
Notice that the third approximation balances the first two a little bit.
So, we'll have that: \(capacity*0.8=140\) > \(capacity=\frac{140}{0.8}=175\).
Hence, the amount of water the reservoirs were short of total capacity prior to the storm was approximately \(175130=45\) billion gallons.
Answer: E. This is my first post on a question, but this question makes me feel really ignorant. I understand most of the concept for finding the answer, but my general math is not strong. When I see \((140/0.8)\), I feel like that is starting to get math heavy and don't have the skills to handle that in my head. Perhaps there is a concept you can point me too to help manipulate such a fraction in my head or another solution not calculation intensive? I feel just as ignorant when I see \(138/82%\), otherwise I get how to solve the problem. Please forgive my ignorance, still new to the journey.



Math Expert
Joined: 02 Sep 2009
Posts: 50007

Re: A rainstorm increased the amount of water stored in State J
[#permalink]
Show Tags
17 Mar 2015, 07:27
braveally wrote: Bunuel wrote: SOLUTION
A rainstorm increased the amount of water stored in State J reservoirs from 124 billion gallons to 138 billion gallons. If the storm increased the amount of water in the reservoirs to 82 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm?
(A) 9 (B) 14 (C) 25 (D) 30 (E) 44
Since we need to find only an approximate value and the answer choices are quite widespread, then use:
80% instead of 82% (notice that this approximation gives the bigger tank capacity); 140 billion gallons instead of 138 billion gallons (notice that this approximation also gives the bigger tank capacity); 130 billion gallons instead of 124 billion gallons;.
Notice that the third approximation balances the first two a little bit.
So, we'll have that: \(capacity*0.8=140\) > \(capacity=\frac{140}{0.8}=175\).
Hence, the amount of water the reservoirs were short of total capacity prior to the storm was approximately \(175130=45\) billion gallons.
Answer: E. This is my first post on a question, but this question makes me feel really ignorant. I understand most of the concept for finding the answer, but my general math is not strong. When I see \((140/0.8)\), I feel like that is starting to get math heavy and don't have the skills to handle that in my head. Perhaps there is a concept you can point me too to help manipulate such a fraction in my head or another solution not calculation intensive? I feel just as ignorant when I see \(138/82%\), otherwise I get how to solve the problem. Please forgive my ignorance, still new to the journey. There are several ways: \(\frac{140}{0.8}=\frac{1400}{8}= 175\); \(\frac{140}{0.8}=\frac{140}{(\frac{4}{5})}= 140*\frac{5}{4}=175\).
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 09 Apr 2014
Posts: 4

Re: A rainstorm increased the amount of water stored in State J
[#permalink]
Show Tags
17 Mar 2015, 08:05
That clears it up, thanks Bunuel. Recognizing 0.8 as 4/5 is a lot easier for me to handle this question.



Intern
Joined: 11 Nov 2014
Posts: 36
Concentration: Marketing, Finance
WE: Programming (Computer Software)

A rainstorm increased the amount of water stored in State J
[#permalink]
Show Tags
02 May 2016, 04:35
The question says 138 is the 82% of the total capacity of reservoir. for simplifications  I took 138 as 140 and 82% as 83.33%(which as a fraction is 5/6). Now you can do the easy calculations  5/6 of the reservoir is 140 gallon then whole capacity (1) of the reservoir will be 140*6/5 = 168 gallon Now we are asked how many gallon was short prior to the storm  168  124 = 44. pretty easy right!?



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830

Re: A rainstorm increased the amount of water stored in State J
[#permalink]
Show Tags
02 May 2016, 07:14
Bunuel wrote: A rainstorm increased the amount of water stored in State J reservoirs from 124 billion gallons to 138 billion gallons. If the storm increased the amount of water in the reservoirs to 82 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm? (A) 9 (B) 14 (C) 25 (D) 30 (E) 44 Practice Questions Question: 6 Page: 152 Difficulty: 600 Solution: We are given that the water increased from 124 billion gallons to 138 billion gallons. We also know that 138 billion gallons is 82% of the total capacity. Let’s translate this information into an equation, where T = total capacity. We translate the sentence "138 billion gallons is 82% of total capacity" as 138 = (0.82)T, remembering that "is" means "equals" and "of" means "multiply." However, we are told to APPROXIMATE. So, instead of using the equation 0.82T = 138, we can instead use 0.8T = 136. Note that I chose 136 because I know that it is divisible by 8, but you could just as easily use 138 and ignore the decimal values. Now we need to solve for T. T = 136/0.8 T = 1360/8 T = 170 The total capacity is approximately 170 billion gallons. It follows that the reservoirs were approximately 170 – 124 = 46 billion gallons short of capacity prior to the storm. From our approximated answer, we see that answer choice E (44) is closest. Answer E.
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



SVP
Joined: 06 Nov 2014
Posts: 1883

Re: A rainstorm increased the amount of water stored in State J
[#permalink]
Show Tags
30 May 2016, 21:03
Assume the total capacity = 100x billion gallons Given that 138 billion gallons = 82x
x = 138/82 = 1.68 Total water = 168 billion gallons Initial water level was 168  124 = 44 billion gallons short of the capacity
Correct Option: E
We can also approximate the values to get the answer approximately. x = 138/82 = 140/80 = 1.7 (Note that since we have increased the numerator and decreased the denominator, the final value will be larger) Total water = 170 billion gallons Difference = 170  124 = 46 billion gallons. Only option E is the closest.



Senior Manager
Joined: 18 Jan 2010
Posts: 252

Re: A rainstorm increased the amount of water stored in State J
[#permalink]
Show Tags
30 May 2016, 21:50
Bunuel wrote: A rainstorm increased the amount of water stored in State J reservoirs from 124 billion gallons to 138 billion gallons. If the storm increased the amount of water in the reservoirs to 82 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm?
(A) 9 (B) 14 (C) 25 (D) 30 (E) 44
so 82 % of total capacity = 138 gallons. so Total capacity = (138 / 0.82) Shortage = (138/0.82)  124 = 172.5  124 = 48. Answer : E



Senior Manager
Joined: 18 Jan 2010
Posts: 252

Re: A rainstorm increased the amount of water stored in State J
[#permalink]
Show Tags
30 May 2016, 21:50
Bunuel wrote: A rainstorm increased the amount of water stored in State J reservoirs from 124 billion gallons to 138 billion gallons. If the storm increased the amount of water in the reservoirs to 82 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm?
(A) 9 (B) 14 (C) 25 (D) 30 (E) 44
so 82 % of total capacity = 138 gallons. so Total capacity = (138 / 0.82) Shortage = (138/0.82)  124 = 172.5  124 = 48. Answer : E



Director
Joined: 09 Mar 2016
Posts: 942

A rainstorm increased the amount of water stored in State J
[#permalink]
Show Tags
14 Apr 2018, 05:07
Bunuel wrote: SOLUTION
A rainstorm increased the amount of water stored in State J reservoirs from 124 billion gallons to 138 billion gallons. If the storm increased the amount of water in the reservoirs to 82 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm?
(A) 9 (B) 14 (C) 25 (D) 30 (E) 44
Since we need to find only an approximate value and the answer choices are quite widespread, then use:
80% instead of 82% (notice that this approximation gives the bigger tank capacity); 140 billion gallons instead of 138 billion gallons (notice that this approximation also gives the bigger tank capacity); 130 billion gallons instead of 124 billion gallons;.
Notice that the third approximation balances the first two a little bit.
So, we'll have that: \(capacity*0.8=140\) > \(capacity=\frac{140}{0.8}=175\).
Hence, the amount of water the reservoirs were short of total capacity prior to the storm was approximately \(175130=45\) billion gallons.
Answer: E. Bunuel is my apprach corect ? 138= 80% 124 =x cross multiply x = 61% hence 124= 61% so 14 billion equals 19% percent increase then.... but in this case if initial number is 124 and it is 61 % and and 14 is abt 19 % then to reacg one 100% we need to double 14*2 which is abt 30:? oops something went wrong where did i make mistake pushpitkc hi can you please explain where am I wrong ?



Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3188
Location: India
GPA: 3.12

Re: A rainstorm increased the amount of water stored in State J
[#permalink]
Show Tags
15 Apr 2018, 10:38
dave13 wrote: Bunuel wrote: SOLUTION
A rainstorm increased the amount of water stored in State J reservoirs from 124 billion gallons to 138 billion gallons. If the storm increased the amount of water in the reservoirs to 82 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm?
(A) 9 (B) 14 (C) 25 (D) 30 (E) 44
Since we need to find only an approximate value and the answer choices are quite widespread, then use:
80% instead of 82% (notice that this approximation gives the bigger tank capacity); 140 billion gallons instead of 138 billion gallons (notice that this approximation also gives the bigger tank capacity); 130 billion gallons instead of 124 billion gallons;.
Notice that the third approximation balances the first two a little bit.
So, we'll have that: \(capacity*0.8=140\) > \(capacity=\frac{140}{0.8}=175\).
Hence, the amount of water the reservoirs were short of total capacity prior to the storm was approximately \(175130=45\) billion gallons.
Answer: E. Bunuel is my apprach corect ? 138= 80% 124 =x cross multiply x = 61%hence 124= 61% so 14 billion equals 19% percent increase then.... but in this case if initial number is 124 and it is 61 % and and 14 is abt 19 % then to reacg one 100% we need to double 14*2 which is abt 30:? oops something went wrong where did i make mistake pushpitkc hi can you please explain where am I wrong ? Hi dave13Please check your math on the highlighted portion  If 138 is 80%, 124 must be 72%(apprx) This makes the difference of 14 about 8%. In order to bring the tank to capacity(100%), we would need an increase of 20%  which is around 35+ The only answer option greater than 30 is Option E(44) Hope this helps you!
_________________
You've got what it takes, but it will take everything you've got




Re: A rainstorm increased the amount of water stored in State J &nbs
[#permalink]
15 Apr 2018, 10:38






